I have analyzed children´s math skill development across a three year period (from preschool to primary school) six measurement point)using LGM. Because children´s skills develop rapidly during this particular period, I have not been able to use identical measurement during each measurement point, i.e., although the structure of the test was identical at all measurement points (5 subscales; progressively more difficult across the test), more difficult items were added to some of the subscales as the children became more skilled in mathematics. This was done in order to avoid a ceiling effect across measurement points.

I wonder if it is possible to use LGM in this case (the construct is assumed to be the same but there is more items in some subscales in subsequent measurement points than in earlier ones)? If I use only those items that were identical at each measurement point, there would be a ceiling effect. Would Item Response theory hepl here? Any suggestions how I should proceed?

Yes, LGM can be used here. You can take several approaches. Here are 2 key ones. In either approach it doesn't matter that you have different number of items at the different time points. First, if you have a large number of items (large number refers to the total number of items if you believe in one factor for all 5 subscales, and refers to number of items per subscale if each subscale is a factor), you can use IRT in line with books like Hambleton-Swaminathan and use the common items across time to produce ability scores ("theta" estimates, or "factor scores") for each child that are in the same metric across time. Then do LGM with these scores as outcomes. Second, if you have a smaller number of items you may want to do multiple-indicator growth modeling with the items as outcomes, where you hold item parameters equal across time for common items.

Dear Linda, I am new to IRT, I came across the idea of ceiling and floor effect as it seems important using this approach. I am following example 5.5 for my 10 binary variables. I have nearly one third of my sample of(1000 subjects) who responded with zero to all items. I have got estimates of the zscores for all the subjects. I am not very sure whether this is ok! & how these values were estimated using the MLH approach. Please advice on: 1- whether Mplus would have used certain approximation to obtain these estimates? & 2- suitable reference for details of these estimates, please! with thanks

I think you are equating IRT with categorical data modeling. If you have floor or ceiling effects, you should use categorical data modeling. This is done by putting the dependent variables on the CATEGORICAL list and using either weighted least squares or maximum likelihood estimation. IRT uses maximum likelihood.

Hi- I am trying to estimate a LGM with 4 time points but I'm not sure how best to treat my observed data. Each wave has an ordered categorical scale that has a bimodal distribution- more responses at both ends of the scale.

I'm planning several time variant and invariant covariates. So I am apprehensive about treating the data as categorical due to the increased computational intensity and difficulty interpreting effects of covariates. But given the distribution, I don't know that treating them as continuous is even possible to interpret.

I would not treat an ordered categorical variable with floor and ceiling effects as continuous. I would treat it is categorical. I don't think this model should be that computationally demanding. As far as the covariates go, you can look at only sign and significance if you don't wish to take it any further.